Over cooking (as in sprouts LOL) destroys the vitamins and minerals, so you throw em out with the water when you strain em.
The GI is a bit different; like mashed spud being faster acting than a boiled spud. That's to do with the mashing of it breaking down the remaining cellulose round the starch in spuds - and it may be the same with cauli?
Not the actual carb CONTENT per se; more the AVAILABLE carb content ? Because your body doesn't have to do much to get to the carb, it can get at it (and it to you!) quicker.
Probably if you ate a tablespoon of flour it wouldn't get into your bloodstream very quickly (I'm not about to try it!) BUT the whole basis of boiling the flour (as in thickening a sauce) is to cause the gluten to be released - so you know whenever you do that you have released a tablespoon of immediately available carb, that when you put it in your mouth, your body can absorb pronto.
A roux will be faster acting carb than a beurre manie for example because the first one involves hot fat which breaks down the cellulose and the second, cold fat which only does it slightly as you work it.
I'm sure Heston could explain thisa lot better than me .....
But finally, the sauce thickened with cauli will always be lower carb than with flour because there's less carb in cauli whatever you do to them - unless you eat a field of em!